a.k.a. WitEden Super Magic Cube Made by WitEden, sold by Mefferts 2011.
(plastic, 2.25" x 2.25" x 1.75"; also sold in a white body)

In the same theme of
Rubik's Cube 3x3x3
generalized to the
Crazy Cube 3x3x3,
this puzzle generalizes the WitEden 3x3 stacks
(that were made as large as
3x3x9)
to have the added movement.
For this one,
the circle turns with the top layer,
and the bottom layer turns around the circle;
a version was also made where both the top and bottom layers turn around the circle.